Effect of Interfacial Pressure Jump and Virtual Mass Terms on Sound Wave Propagation in the Two-Phase Flow

On the Wave Dispersion Relevant to the Virtual Mass Terms in the Two-Phase Two-Fluid Model

“…The averaged bubble diam eter D ave is genera lly obta ined by using the Weber number definit ion, We == 2D ave Pl l' g -1', )2 Ia . However, if we simply ass ume tha t two rad ii R g an d R, are eq ual to hal f of the averaged bubble dia me ter D ave ' then th e coefficient of inter facial pressur e jump C j become s consta nt having an o rde r of magn itude 0 (10-1 ) : See Ch ung et al [9].…”

“…Th e interfacial pressure j ump ter ms reformula ted by Chung et al [9] have also co ntributed to the hyperb olic type of the govern ing equa tion system for the bu bbly flow. Th e sound speed in the two-phase mixture evaluated by the real eigenva lues showe d excellent agreement with the existin g experimental dat a .…”

On the hyperbolicity of the two-fluid model for gas–liquid bubbly flows

“…Some authors [11][12][13] performed numerical regularization of the ill-posed equation, which, however, comes at the expense of accuracy, since it relies on the addition of numerical dissipation. Several investigators [6,9,[14][15][16][17][18][19] ensured the hyperbolicity of the two-fluid model by introducing a pressure term in the phase momentum equation. The presence of the same mean bulk pressure P k in both the phases was assumed in [6], and added an interface pressure term (p ki − P k ) ∇α, where p ki is the interface pressure for phase k, in order to make the two-fluid model hyperbolic.…”

Effect of Virtual Mass Force on the Mixed Transport Process in a Multiphase Rotodynamic Pump

“…For example, by introducing the virtual mass force term in a three-fluid model for the annular flow inside condensing steam pipes, Hamid and Nemat improved the pressure drop predictions [2]. From the point of numerical simulation, the virtual mass term retained in the momentum equations helps to improve the numerical stability of the initial value problems, extending the parameter range in which the equation system yields real eigenvalues [3].…”

“…In addition, some unknown phenomena may also occur in the gasliquid mixed transport process. For example, in the study of sound wave propagation in two-phase flow, it is found that the virtual mass terms can cause nonphysical dispersion [3]. To investigate the effect of virtual mass force on the mixed transport process in a multiphase rotodynamic pump, unsteady simulation based on two-fluid model is carried out in this paper.…”